An 18-disk RAID5 is a train wreck waiting to happen... I hope you have a good backup.
Seriously, you need to use RAID6 for anything beyond 5 disks maximum or disks larger than 1 TB.
Since you don't have the option to shrink the array, you'd need to add disks so you can migrate to RAID6, with or without hot spare. With 18 disks I'd seriously suggest using a RAID60 with nine-disk subarrays (thx @Nikita).
we no longer have a configuration offering us the ability to recover from 2 lost drives
You never had. RAID5 with host spare can recover from one lost drive and after rebuilding may recover from another lost drive. If anything happens during rebuild - which isn't uncommon - the array is lost.
there's no 19th slot to install a dedicated hot spare.
If you can't add drives, you're pretty much out of space anyway. Either test your backup-and-recovery scheme, deleting and creating a RAID6 or - better - RAID60 array this time, or consider migrating to a new server.
If there's no budget and no maintenance window for recreating the array you're pretty much out of options. Make sure there's reliable and well-tested backup (two backup instances, on different media, testing including bare-metal recovery), run regular scrubbing (significantly reducing the chance to hit stale data errors while rebuilding), stop the reseating practice (which might have gotten you into this pickle in the first place), and hold your thumbs. You're running on fumes.
By the way, have you estimated the cost and scenario of the array failing altogether?